Technically, yes. However, the reality is that clubs can and have ignored release clauses before.
Look at Suarez and Liverpool - Arsenal bid 1 pound above his release clause (I think a total of 40,000,001), and that was supposed to trigger it.
Liverpool ignored it - very publicly so. Because they gambled that Suarez wouldn't take them to the Court of Arbitration for Sport over a move to Arsenal of all places. And, if he did, they could argue that Arsenal knowing about the clause was in itself a violation of Suarez's contract, because that entailed that they had tapped him up behind the scenes or talked to his agent.
In that case, they gambled right, and Suarez didn't mind that they ignored his release clause in that instance. But it really does depend on the relationship between the selling club, the bidding club and the player.